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Posted 02 April 2013 - 06:11 PM

Given four points A, B, C, D, and four directly similar quadrilaterals AP1P2B, CQ1Q2B, CR1R2D, AS1S2D with respective centroids P, Q, R, S, let K, L, M, and N be the midpoints of the segments P1Q2, Q1R2, R1S2 and S1P2 respectively (or of P1S2, S1R2, R1Q2 and Q1P2), and let V, W, X be the centroids of the quadrilaterals ABCD, PQRS, KLMN respectively.

Then what is special about PQRS, KLMN, and point W?

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Posted 08 April 2013 - 11:13 PM

Spoiler for 1 of the answers

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### #3 bonanova

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Posted 11 April 2013 - 11:37 PM

Given four points A, B, C, D, and four directly similar quadrilaterals AP1P2B,

I'm struggling with picturing these similar quadrilaterals.

Proportional sides are needed, No?

If AB is common, which sides are proportional?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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Posted 12 April 2013 - 01:45 AM

There are 5 ways to prove a Quadrilateral is a Parallelogram.

-Prove both pairs of opposite sides congruent

-Prove both pairs of opposite sides parallel

-Prove one pair of opposite sides both congruent and parallel

-Prove both pairs of opposite angles are congruent

-Prove that the diagonals bisect each other

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Posted 12 April 2013 - 01:59 AM

here is the figure of what i am talking about

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Posted 12 April 2013 - 02:18 AM

Spoiler for it may help to prove this theorem first

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